While there is no rule that says that you cannot have two templated links to your home page via an image and then navigation, I would advise against it as a rule. As well, I advise against creating two different links to any page within your template design generally. However, this is sometimes done in places such as the footer and this is okay. Google will only use the first one found in most cases and ignore the remaining. More on that later.
You are far better off with the navigational link. The reason is simple. The navigational link provides significantly greater advantages over an image link. I write about the differences here: Images as hyperlinks and SEO implications The up-shot is that there are semantic advantages to a text based link over any other link.
There is no boost for having more than one link of any kind to your home page. This is just plain bad advice.
Google takes the first link to any target page found in a source page and uses that link and ignores the remaining links. Under certain circumstances, Google may chose another link if it feels that it is a better link, however, it still only chooses one that represents that target. This means that there are two things that can happen: one, Google can chose the generally lower value image link; and two, Google may not recognize your navigational link which can effect things such as site links.
With links to any target page, semantics is extremely important. You lose this advantage with an image link. The link text is always more important will always outweigh any image alt text. As well, Google values navigational links higher as a signal to important pages. This has an important cascading effect that you do not want to defeat. If Google takes your image link over your navigational link, you lose these advantages.
Nofollow is an important tool, however, generally should not be used except to protect areas of your site that should not be indexed. A nofollow link does not fully protect these areas of your site if there are other links. Normally, a nofollow and noindex are used in conjunction to protect areas of your site you need to protect. Using nofollow will not help in signalling which link is better than any other or with SEO.
Google will likely see multiple links to a page and links with nofollow as link sculpting which is an old black-hat technique that does not work. You want to avoid issues where Google thinks you are sculpting links. Google does apply a penalty for link sculpting that is hard to escape.
If you are to have multiple links to any page for which you have a navigational link for, make sure that your navigational link is found first. All others will be ignored and the navigational link will provide an important signal to Google that the pages linked from your navigational links are important. You can have other links of course, just know that there is no real advantage except for user experience (UX). Under no circumstances should you have nofollow links from your home page except in conjunction with noindex to protect areas of your site that should not appear in the SERPs.